LMFDB - Embedded newform 1764.2.l.j.949.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1764.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			949.11
Character	$\chi$	$=$	1764.949
Dual form			1764.2.l.j.961.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52658 - 0.818256i) q^{3} -3.89246 q^{5} +(1.66092 - 2.49827i) q^{9} +4.37557 q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +(-2.66678 + 4.61900i) q^{17} +(-2.32161 - 4.02115i) q^{19} +0.367799 q^{23} +10.1513 q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +(-1.14776 - 1.98798i) q^{31} +(6.67967 - 3.58033i) q^{33} +(-5.44017 - 9.42265i) q^{37} +(0.0866059 - 2.74290i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(-6.46505 + 9.72443i) q^{45} +(-3.80432 + 6.58928i) q^{47} +(-0.291541 + 9.23339i) q^{51} +(0.462847 - 0.801674i) q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +(-0.460475 - 0.797565i) q^{59} +(3.27780 - 5.67731i) q^{61} +(-3.08361 + 5.34097i) q^{65} +(-7.50420 - 12.9976i) q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} +(3.78353 - 6.55327i) q^{73} +(15.4968 - 8.30634i) q^{75} +(-0.987715 + 1.71077i) q^{79} +(-3.48272 - 8.29883i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(-14.9768 - 9.28908i) q^{87} +(-6.10987 - 10.5826i) q^{89} +(-3.37883 - 2.09566i) q^{93} +(9.03679 + 15.6522i) q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95}+ \cdots - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.52658	−	0.818256i	0.881373	−	0.472420i
$3$	1.52658	−	0.818256i	0.881373	−	0.472420i
$4$		0			0
$5$	−3.89246			−1.74076			−0.870381	−	0.492378i	$-0.836128\pi$
$5$	−3.89246			−1.74076			−0.870381	+	0.492378i	$0.836128\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.66092	−	2.49827i	0.553638	−	0.832757i
$10$		0			0
$11$	4.37557			1.31928			0.659642	−	0.751580i	$-0.270708\pi$
$11$	4.37557			1.31928			0.659642	+	0.751580i	$0.270708\pi$
$12$		0			0
$13$	0.792201	−	1.37213i	0.219717	−	0.380561i	−0.735004	−	0.678062i	$-0.762820\pi$
$13$	0.792201	−	1.37213i	0.219717	−	0.380561i	0.954721	+	0.297501i	$0.0961533\pi$
$14$		0			0
$15$	−5.94217	+	3.18503i	−1.53426	+	0.822371i
$16$		0			0
$17$	−2.66678	+	4.61900i	−0.646789	+	1.12027i	0.337096	+	0.941470i	$0.390555\pi$
$17$	−2.66678	+	4.61900i	−0.646789	+	1.12027i	−0.983885	+	0.178801i	$0.942778\pi$
$18$		0			0
$19$	−2.32161	−	4.02115i	−0.532614	−	0.922515i	−0.999275	−	0.0380786i	$-0.987876\pi$
$19$	−2.32161	−	4.02115i	−0.532614	−	0.922515i	0.466660	−	0.884437i	$-0.345457\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.367799			0.0766914			0.0383457	−	0.999265i	$-0.487791\pi$
$23$	0.367799			0.0766914			0.0383457	+	0.999265i	$0.487791\pi$
$24$		0			0
$25$	10.1513			2.03025
$26$		0			0
$27$	0.491301	−	5.17287i	0.0945509	−	0.995520i
$28$		0			0
$29$	−5.08750	−	8.81180i	−0.944724	−	1.63631i	−0.756302	−	0.654222i	$-0.772996\pi$
$29$	−5.08750	−	8.81180i	−0.944724	−	1.63631i	−0.188422	−	0.982088i	$-0.560337\pi$
$30$		0			0
$31$	−1.14776	−	1.98798i	−0.206144	−	0.357052i	0.744353	−	0.667787i	$-0.232758\pi$
$31$	−1.14776	−	1.98798i	−0.206144	−	0.357052i	−0.950497	+	0.310735i	$0.899425\pi$
$32$		0			0
$33$	6.67967	−	3.58033i	1.16278	−	0.623256i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.44017	−	9.42265i	−0.894359	−	1.54907i	−0.834596	−	0.550862i	$-0.814299\pi$
$37$	−5.44017	−	9.42265i	−0.894359	−	1.54907i	−0.0597623	−	0.998213i	$-0.519034\pi$
$38$		0			0
$39$	0.0866059	−	2.74290i	0.0138680	−	0.439215i
$40$		0			0
$41$	0.690443	−	1.19588i	0.107829	−	0.186766i	−0.807061	−	0.590467i	$-0.798943\pi$
$41$	0.690443	−	1.19588i	0.107829	−	0.186766i	0.914891	+	0.403702i	$0.132277\pi$
$42$		0			0
$43$	3.81699	+	6.61122i	0.582086	+	1.00820i	0.995232	+	0.0975372i	$0.0310965\pi$
$43$	3.81699	+	6.61122i	0.582086	+	1.00820i	−0.413146	+	0.910665i	$0.635570\pi$
$44$		0			0
$45$	−6.46505	+	9.72443i	−0.963753	+	1.44963i
$46$		0			0
$47$	−3.80432	+	6.58928i	−0.554918	+	0.961145i	0.442992	+	0.896525i	$0.353917\pi$
$47$	−3.80432	+	6.58928i	−0.554918	+	0.961145i	−0.997910	+	0.0646200i	$0.979416\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.291541	+	9.23339i	−0.0408239	+	1.29293i
$52$		0			0
$53$	0.462847	−	0.801674i	0.0635769	−	0.110118i	−0.832485	−	0.554048i	$-0.813083\pi$
$53$	0.462847	−	0.801674i	0.0635769	−	0.110118i	0.896062	+	0.443929i	$0.146416\pi$
$54$		0			0
$55$	−17.0317			−2.29656
$56$		0			0
$57$	−6.83447	−	4.23895i	−0.905247	−	0.561463i
$58$		0			0
$59$	−0.460475	−	0.797565i	−0.0599487	−	0.103834i	0.834493	−	0.551018i	$-0.185760\pi$
$59$	−0.460475	−	0.797565i	−0.0599487	−	0.103834i	−0.894442	+	0.447184i	$0.852427\pi$
$60$		0			0
$61$	3.27780	−	5.67731i	0.419679	−	0.726905i	−0.576228	−	0.817289i	$-0.695476\pi$
$61$	3.27780	−	5.67731i	0.419679	−	0.726905i	0.995907	+	0.0903836i	$0.0288093\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.08361	+	5.34097i	−0.382475	+	0.662466i
$66$		0			0
$67$	−7.50420	−	12.9976i	−0.916783	−	1.58792i	−0.804269	−	0.594265i	$-0.797443\pi$
$67$	−7.50420	−	12.9976i	−0.916783	−	1.58792i	−0.112514	−	0.993650i	$-0.535890\pi$
$68$		0			0
$69$	0.561476	−	0.300954i	0.0675938	−	0.0362306i
$70$		0			0
$71$	−4.91059			−0.582780			−0.291390	−	0.956604i	$-0.594118\pi$
$71$	−4.91059			−0.582780			−0.291390	+	0.956604i	$0.594118\pi$
$72$		0			0
$73$	3.78353	−	6.55327i	0.442829	−	0.767003i	−0.555069	−	0.831804i	$-0.687308\pi$
$73$	3.78353	−	6.55327i	0.442829	−	0.767003i	0.997898	+	0.0648016i	$0.0206415\pi$
$74$		0			0
$75$	15.4968	−	8.30634i	1.78941	−	0.959133i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.987715	+	1.71077i	−0.111127	+	0.192477i	−0.916225	−	0.400665i	$-0.868779\pi$
$79$	−0.987715	+	1.71077i	−0.111127	+	0.192477i	0.805098	+	0.593142i	$0.202113\pi$
$80$		0			0
$81$	−3.48272	−	8.29883i	−0.386969	−	0.922093i
$82$		0			0
$83$	0.253011	+	0.438227i	0.0277715	+	0.0481017i	0.879577	−	0.475756i	$-0.157826\pi$
$83$	0.253011	+	0.438227i	0.0277715	+	0.0481017i	−0.851806	+	0.523858i	$0.824492\pi$
$84$		0			0
$85$	10.3803	−	17.9793i	1.12591	−	1.95013i
$86$		0			0
$87$	−14.9768	−	9.28908i	−1.60568	−	0.995894i
$88$		0			0
$89$	−6.10987	−	10.5826i	−0.647645	−	1.12175i	−0.983684	−	0.179906i	$-0.942421\pi$
$89$	−6.10987	−	10.5826i	−0.647645	−	1.12175i	0.336039	−	0.941848i	$-0.390913\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.37883	−	2.09566i	−0.350369	−	0.217310i
$94$		0			0
$95$	9.03679	+	15.6522i	0.927155	+	1.60588i
$96$		0			0
$97$	−4.45315	−	7.71308i	−0.452149	−	0.783145i	0.546370	−	0.837544i	$-0.316009\pi$
$97$	−4.45315	−	7.71308i	−0.452149	−	0.783145i	−0.998519	+	0.0543987i	$0.982676\pi$
$98$		0			0
$99$	7.26745	−	10.9314i	0.730406	−	1.09864i
$100$		0			0
$101$	−11.0236			−1.09689			−0.548445	−	0.836187i	$-0.684780\pi$
$101$	−11.0236			−1.09689			−0.548445	+	0.836187i	$0.684780\pi$
$102$		0			0
$103$	−2.73085			−0.269079			−0.134540	−	0.990908i	$-0.542956\pi$
$103$	−2.73085			−0.269079			−0.134540	+	0.990908i	$0.542956\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.39605	+	9.34623i	0.521655	+	0.903534i	0.999683	+	0.0251887i	$0.00801867\pi$
$107$	5.39605	+	9.34623i	0.521655	+	0.903534i	−0.478027	+	0.878345i	$0.658648\pi$
$108$		0			0
$109$	4.99187	−	8.64617i	0.478134	−	0.828153i	−0.521551	−	0.853220i	$-0.674647\pi$
$109$	4.99187	−	8.64617i	0.478134	−	0.828153i	0.999686	+	0.0250668i	$0.00797984\pi$
$110$		0			0
$111$	−16.0150	−	9.93302i	−1.52008	−	0.942800i
$112$		0			0
$113$	−6.12019	+	10.6005i	−0.575739	+	0.997209i	0.420222	+	0.907421i	$0.361952\pi$
$113$	−6.12019	+	10.6005i	−0.575739	+	0.997209i	−0.995961	+	0.0897875i	$0.971381\pi$
$114$		0			0
$115$	−1.43164			−0.133502
$116$		0			0
$117$	−2.11218	−	4.25813i	−0.195271	−	0.393664i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.14559			0.740509
$122$		0			0
$123$	0.0754814	−	2.39057i	0.00680593	−	0.215551i
$124$		0			0
$125$	−20.0511			−1.79343
$126$		0			0
$127$	−13.2005			−1.17135			−0.585677	−	0.810544i	$-0.699171\pi$
$127$	−13.2005			−1.17135			−0.585677	+	0.810544i	$0.699171\pi$
$128$		0			0
$129$	11.2366	+	6.96931i	0.989330	+	0.613613i
$130$		0			0
$131$	−5.08683			−0.444438			−0.222219	−	0.974997i	$-0.571330\pi$
$131$	−5.08683			−0.444438			−0.222219	+	0.974997i	$0.571330\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.91237	+	20.1352i	−0.164591	+	1.73296i
$136$		0			0
$137$	13.3442			1.14007			0.570034	−	0.821621i	$-0.306930\pi$
$137$	13.3442			1.14007			0.570034	+	0.821621i	$0.306930\pi$
$138$		0			0
$139$	4.85642	−	8.41157i	0.411916	−	0.713460i	−0.583183	−	0.812341i	$-0.698193\pi$
$139$	4.85642	−	8.41157i	0.411916	−	0.713460i	0.995099	+	0.0988809i	$0.0315263\pi$
$140$		0			0
$141$	−0.415901	+	13.1720i	−0.0350251	+	1.10928i
$142$		0			0
$143$	3.46633	−	6.00386i	0.289869	−	0.502068i
$144$		0			0
$145$	19.8029	+	34.2996i	1.64454	+	2.84843i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.8423			1.13401			0.567004	−	0.823715i	$-0.308102\pi$
$149$	13.8423			1.13401			0.567004	+	0.823715i	$0.308102\pi$
$150$		0			0
$151$	22.8759			1.86162			0.930809	−	0.365506i	$-0.119104\pi$
$151$	22.8759			1.86162			0.930809	+	0.365506i	$0.119104\pi$
$152$		0			0
$153$	7.11022	+	14.3341i	0.574827	+	1.15884i
$154$		0			0
$155$	4.46762	+	7.73815i	0.358848	+	0.621543i
$156$		0			0
$157$	5.78991	+	10.0284i	0.462085	+	0.800355i	0.999065	−	0.0432404i	$-0.0137681\pi$
$157$	5.78991	+	10.0284i	0.462085	+	0.800355i	−0.536980	+	0.843595i	$0.680435\pi$
$158$		0			0
$159$	0.0505998	−	1.60255i	0.00401283	−	0.127090i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.70577	−	2.95449i	−0.133607	−	0.231413i	0.791458	−	0.611224i	$-0.209323\pi$
$163$	−1.70577	−	2.95449i	−0.133607	−	0.231413i	−0.925064	+	0.379811i	$0.875989\pi$
$164$		0			0
$165$	−26.0004	+	13.9363i	−2.02413	+	1.08494i
$166$		0			0
$167$	4.69996	−	8.14057i	0.363694	−	0.629936i	−0.624872	−	0.780727i	$-0.714849\pi$
$167$	4.69996	−	8.14057i	0.363694	−	0.629936i	0.988566	+	0.150791i	$0.0481821\pi$
$168$		0			0
$169$	5.24484	+	9.08432i	0.403449	+	0.698794i
$170$		0			0
$171$	−13.9019	−	0.878772i	−1.06311	−	0.0672014i
$172$		0			0
$173$	−3.20256	+	5.54700i	−0.243486	+	0.421730i	−0.961705	−	0.274087i	$-0.911624\pi$
$173$	−3.20256	+	5.54700i	−0.243486	+	0.421730i	0.718219	+	0.695817i	$0.244958\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.35557	−	0.840764i	−0.101891	−	0.0631957i
$178$		0			0
$179$	−8.54038	+	14.7924i	−0.638338	+	1.10563i	0.347460	+	0.937695i	$0.387044\pi$
$179$	−8.54038	+	14.7924i	−0.638338	+	1.10563i	−0.985797	+	0.167938i	$0.946289\pi$
$180$		0			0
$181$	−1.35988			−0.101079			−0.0505395	−	0.998722i	$-0.516094\pi$
$181$	−1.35988			−0.101079			−0.0505395	+	0.998722i	$0.516094\pi$
$182$		0			0
$183$	0.358339	−	11.3490i	0.0264892	−	0.838940i
$184$		0			0
$185$	21.1757	+	36.6773i	1.55687	+	2.69657i
$186$		0			0
$187$	−11.6687	+	20.2107i	−0.853298	+	1.47796i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.94048	−	15.4854i	0.646911	−	1.12048i	−0.336946	−	0.941524i	$-0.609394\pi$
$191$	8.94048	−	15.4854i	0.646911	−	1.12048i	0.983857	−	0.178958i	$-0.0572727\pi$
$192$		0			0
$193$	6.50664	+	11.2698i	0.468358	+	0.811220i	0.999346	−	0.0361591i	$-0.0115123\pi$
$193$	6.50664	+	11.2698i	0.468358	+	0.811220i	−0.530988	+	0.847380i	$0.678179\pi$
$194$		0			0
$195$	−0.337110	+	10.6766i	−0.0241410	+	0.764569i
$196$		0			0
$197$	6.36486			0.453478			0.226739	−	0.973956i	$-0.427194\pi$
$197$	6.36486			0.453478			0.226739	+	0.973956i	$0.427194\pi$
$198$		0			0
$199$	11.5764	−	20.0510i	0.820631	−	1.42137i	−0.0845818	−	0.996417i	$-0.526955\pi$
$199$	11.5764	−	20.0510i	0.820631	−	1.42137i	0.905213	−	0.424958i	$-0.139711\pi$
$200$		0			0
$201$	−22.0912	−	13.7016i	−1.55819	−	0.966440i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.68753	+	4.65493i	−0.187705	+	0.325114i
$206$		0			0
$207$	0.610883	−	0.918862i	0.0424593	−	0.0638653i
$208$		0			0
$209$	−10.1584	−	17.5948i	−0.702669	−	1.21706i
$210$		0			0
$211$	−5.67737	+	9.83349i	−0.390846	+	0.676965i	−0.992561	−	0.121745i	$-0.961151\pi$
$211$	−5.67737	+	9.83349i	−0.390846	+	0.676965i	0.601715	+	0.798711i	$0.294484\pi$
$212$		0			0
$213$	−7.49643	+	4.01812i	−0.513647	+	0.275317i
$214$		0			0
$215$	−14.8575	−	25.7339i	−1.01327	−	1.75504i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.413628	−	13.1000i	0.0279504	−	0.885217i
$220$		0			0
$221$	4.22525	+	7.31835i	0.284221	+	0.492285i
$222$		0			0
$223$	13.3206	+	23.0719i	0.892011	+	1.54501i	0.837461	+	0.546498i	$0.184039\pi$
$223$	13.3206	+	23.0719i	0.892011	+	1.54501i	0.0545504	+	0.998511i	$0.482627\pi$
$224$		0			0
$225$	16.8604	−	25.3606i	1.12403	−	1.69071i
$226$		0			0
$227$	16.6027			1.10196			0.550981	−	0.834518i	$-0.314254\pi$
$227$	16.6027			1.10196			0.550981	+	0.834518i	$0.314254\pi$
$228$		0			0
$229$	14.5014			0.958282			0.479141	−	0.877738i	$-0.340948\pi$
$229$	14.5014			0.958282			0.479141	+	0.877738i	$0.340948\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.99020	−	13.8394i	−0.523456	−	0.906652i	−0.999627	−	0.0272993i	$-0.991309\pi$
$233$	−7.99020	−	13.8394i	−0.523456	−	0.906652i	0.476172	−	0.879352i	$-0.342024\pi$
$234$		0			0
$235$	14.8082	−	25.6485i	0.965980	−	1.67313i
$236$		0			0
$237$	−0.107980	+	3.41984i	−0.00701407	+	0.222143i
$238$		0			0
$239$	−9.58994	+	16.6103i	−0.620322	+	1.07443i	0.369104	+	0.929388i	$0.379665\pi$
$239$	−9.58994	+	16.6103i	−0.620322	+	1.07443i	−0.989426	+	0.145040i	$0.953669\pi$
$240$		0			0
$241$	−23.3569			−1.50455			−0.752276	−	0.658848i	$-0.771044\pi$
$241$	−23.3569			−1.50455			−0.752276	+	0.658848i	$0.771044\pi$
$242$		0			0
$243$	−12.1072	−	9.81911i	−0.776679	−	0.629896i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.35673			−0.468098
$248$		0			0
$249$	0.744824	+	0.461963i	0.0472013	+	0.0292757i
$250$		0			0
$251$	30.4619			1.92274			0.961371	−	0.275257i	$-0.0887631\pi$
$251$	30.4619			1.92274			0.961371	+	0.275257i	$0.0887631\pi$
$252$		0			0
$253$	1.60933			0.101178
$254$		0			0
$255$	1.13481	−	35.9407i	0.0710647	−	2.25069i
$256$		0			0
$257$	6.80877			0.424719			0.212360	−	0.977192i	$-0.431885\pi$
$257$	6.80877			0.424719			0.212360	+	0.977192i	$0.431885\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−30.4642	−	1.92571i	−1.88569	−	0.119198i
$262$		0			0
$263$	−4.60001			−0.283649			−0.141824	−	0.989892i	$-0.545297\pi$
$263$	−4.60001			−0.283649			−0.141824	+	0.989892i	$0.545297\pi$
$264$		0			0
$265$	−1.80161	+	3.12049i	−0.110672	+	0.191690i
$266$		0			0
$267$	−17.9865	−	11.1558i	−1.10076	−	0.682724i
$268$		0			0
$269$	−4.25090	+	7.36277i	−0.259182	+	0.448916i	−0.966023	−	0.258456i	$-0.916786\pi$
$269$	−4.25090	+	7.36277i	−0.259182	+	0.448916i	0.706841	+	0.707372i	$0.250120\pi$
$270$		0			0
$271$	3.29191	+	5.70175i	0.199969	+	0.346357i	0.948518	−	0.316723i	$-0.102583\pi$
$271$	3.29191	+	5.70175i	0.199969	+	0.346357i	−0.748549	+	0.663079i	$0.769249\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	44.4176			2.67848
$276$		0			0
$277$	−11.2697			−0.677129			−0.338564	−	0.940943i	$-0.609941\pi$
$277$	−11.2697			−0.677129			−0.338564	+	0.940943i	$0.609941\pi$
$278$		0			0
$279$	−6.87285	−	0.434448i	−0.411467	−	0.0260097i
$280$		0			0
$281$	7.50741	+	13.0032i	0.447854	+	0.775707i	0.998246	−	0.0592000i	$-0.0188550\pi$
$281$	7.50741	+	13.0032i	0.447854	+	0.775707i	−0.550392	+	0.834907i	$0.685522\pi$
$282$		0			0
$283$	7.33657	+	12.7073i	0.436114	+	0.755371i	0.997386	−	0.0722602i	$-0.0230212\pi$
$283$	7.33657	+	12.7073i	0.436114	+	0.755371i	−0.561272	+	0.827631i	$0.689688\pi$
$284$		0			0
$285$	26.6029	+	16.5000i	1.57582	+	0.977373i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.72343	−	9.91327i	−0.336672	−	0.583133i
$290$		0			0
$291$	−13.1094	−	8.13085i	−0.768486	−	0.476639i
$292$		0			0
$293$	9.38981	−	16.2636i	0.548559	−	0.950132i	−0.449815	−	0.893122i	$-0.648510\pi$
$293$	9.38981	−	16.2636i	0.548559	−	0.950132i	0.998374	−	0.0570099i	$-0.0181567\pi$
$294$		0			0
$295$	1.79238	+	3.10449i	0.104356	+	0.180751i
$296$		0			0
$297$	2.14972	−	22.6343i	0.124739	−	1.31337i
$298$		0			0
$299$	0.291371	−	0.504669i	0.0168504	−	0.0291858i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−16.8285	+	9.02013i	−0.966770	+	0.518193i
$304$		0			0
$305$	−12.7587	+	22.0987i	−0.730562	+	1.26537i
$306$		0			0
$307$	28.9425			1.65184			0.825919	−	0.563789i	$-0.190657\pi$
$307$	28.9425			1.65184			0.825919	+	0.563789i	$0.190657\pi$
$308$		0			0
$309$	−4.16888	+	2.23454i	−0.237159	+	0.127118i
$310$		0			0
$311$	−6.79681	−	11.7724i	−0.385412	−	0.667553i	0.606414	−	0.795149i	$-0.292607\pi$
$311$	−6.79681	−	11.7724i	−0.385412	−	0.667553i	−0.991826	+	0.127596i	$0.959274\pi$
$312$		0			0
$313$	−6.93222	+	12.0070i	−0.391832	+	0.678673i	−0.992691	−	0.120682i	$-0.961492\pi$
$313$	−6.93222	+	12.0070i	−0.391832	+	0.678673i	0.600859	+	0.799355i	$0.294825\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.5428	+	19.9927i	−0.648309	+	1.12290i	0.335217	+	0.942141i	$0.391190\pi$
$317$	−11.5428	+	19.9927i	−0.648309	+	1.12290i	−0.983527	+	0.180764i	$0.942143\pi$
$318$		0			0
$319$	−22.2607	−	38.5566i	−1.24636	−	2.15876i
$320$		0			0
$321$	15.8851	+	9.85245i	0.886621	+	0.549910i
$322$		0			0
$323$	24.7649			1.37796
$324$		0			0
$325$	8.04184	−	13.9289i	0.446081	−	0.772635i
$326$		0			0
$327$	0.545727	−	17.2837i	0.0301788	−	0.955793i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.82647	−	13.5558i	0.430182	−	0.745097i	−0.566707	−	0.823920i	$-0.691783\pi$
$331$	7.82647	−	13.5558i	0.430182	−	0.745097i	0.996889	+	0.0788227i	$0.0251161\pi$
$332$		0			0
$333$	−32.5760	−	2.05920i	−1.78515	−	0.112844i
$334$		0			0
$335$	29.2098	+	50.5929i	1.59590	+	2.76418i
$336$		0			0
$337$	3.56686	−	6.17799i	0.194299	−	0.336537i	−0.752371	−	0.658739i	$-0.771090\pi$
$337$	3.56686	−	6.17799i	0.194299	−	0.336537i	0.946671	+	0.322203i	$0.104423\pi$
$338$		0			0
$339$	−0.669078	+	21.1904i	−0.0363393	+	1.15090i
$340$		0			0
$341$	−5.02211	−	8.69855i	−0.271962	−	0.471053i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.18553	+	1.17145i	−0.117665	+	0.0630688i
$346$		0			0
$347$	−2.77827	−	4.81211i	−0.149146	−	0.258328i	0.781766	−	0.623571i	$-0.214319\pi$
$347$	−2.77827	−	4.81211i	−0.149146	−	0.258328i	−0.930912	+	0.365244i	$0.880986\pi$
$348$		0			0
$349$	5.33296	+	9.23696i	0.285467	+	0.494443i	0.972722	−	0.231973i	$-0.0745181\pi$
$349$	5.33296	+	9.23696i	0.285467	+	0.494443i	−0.687256	+	0.726416i	$0.741185\pi$
$350$		0			0
$351$	−6.70866	−	4.77208i	−0.358082	−	0.254715i
$352$		0			0
$353$	12.8426			0.683545			0.341772	−	0.939783i	$-0.388973\pi$
$353$	12.8426			0.683545			0.341772	+	0.939783i	$0.388973\pi$
$354$		0			0
$355$	19.1143			1.01448
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.8417	−	22.2426i	−0.677761	−	1.17392i	−0.975653	−	0.219318i	$-0.929617\pi$
$359$	−12.8417	−	22.2426i	−0.677761	−	1.17392i	0.297892	−	0.954600i	$-0.403716\pi$
$360$		0			0
$361$	−1.27977	+	2.21663i	−0.0673563	+	0.116665i
$362$		0			0
$363$	12.4349	−	6.66518i	0.652665	−	0.349831i
$364$		0			0
$365$	−14.7273	+	25.5084i	−0.770861	+	1.33517i
$366$		0			0
$367$	16.9839			0.886554			0.443277	−	0.896385i	$-0.353816\pi$
$367$	16.9839			0.886554			0.443277	+	0.896385i	$0.353816\pi$
$368$		0			0
$369$	−1.84087	−	3.71118i	−0.0958320	−	0.193196i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.77005			−0.454096			−0.227048	−	0.973884i	$-0.572907\pi$
$373$	−8.77005			−0.454096			−0.227048	+	0.973884i	$0.572907\pi$
$374$		0			0
$375$	−30.6097	+	16.4070i	−1.58068	+	0.847252i
$376$		0			0
$377$	−16.1213			−0.830288
$378$		0			0
$379$	11.7002			0.601001			0.300500	−	0.953782i	$-0.402846\pi$
$379$	11.7002			0.601001			0.300500	+	0.953782i	$0.402846\pi$
$380$		0			0
$381$	−20.1517	+	10.8014i	−1.03240	+	0.553371i
$382$		0			0
$383$	9.00720			0.460246			0.230123	−	0.973162i	$-0.426087\pi$
$383$	9.00720			0.460246			0.230123	+	0.973162i	$0.426087\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	22.8563	+	1.44480i	1.16185	+	0.0734433i
$388$		0			0
$389$	−9.78781			−0.496262			−0.248131	−	0.968727i	$-0.579816\pi$
$389$	−9.78781			−0.496262			−0.248131	+	0.968727i	$0.579816\pi$
$390$		0			0
$391$	−0.980839	+	1.69886i	−0.0496032	+	0.0859152i
$392$		0			0
$393$	−7.76547	+	4.16233i	−0.391716	+	0.209962i
$394$		0			0
$395$	3.84465	−	6.65912i	0.193445	−	0.335057i
$396$		0			0
$397$	6.95929	+	12.0538i	0.349277	+	0.604965i	0.986121	−	0.166027i	$-0.0530940\pi$
$397$	6.95929	+	12.0538i	0.349277	+	0.604965i	−0.636844	+	0.770992i	$0.719761\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−23.4828			−1.17267			−0.586336	−	0.810068i	$-0.699430\pi$
$401$	−23.4828			−1.17267			−0.586336	+	0.810068i	$0.699430\pi$
$402$		0			0
$403$	−3.63703			−0.181173
$404$		0			0
$405$	13.5564	+	32.3029i	0.673621	+	1.60514i
$406$		0			0
$407$	−23.8038	−	41.2295i	−1.17991	−	2.04367i
$408$		0			0
$409$	−6.81225	−	11.7992i	−0.336844	−	0.583431i	0.646993	−	0.762496i	$-0.276026\pi$
$409$	−6.81225	−	11.7992i	−0.336844	−	0.583431i	−0.983837	+	0.179064i	$0.942693\pi$
$410$		0			0
$411$	20.3710	−	10.9189i	1.00483	−	0.538591i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.984835	−	1.70578i	−0.0483436	−	0.0837336i
$416$		0			0
$417$	0.530919	−	16.8148i	0.0259992	−	0.823422i
$418$		0			0
$419$	3.97733	−	6.88894i	0.194305	−	0.336547i	−0.752367	−	0.658744i	$-0.771088\pi$
$419$	3.97733	−	6.88894i	0.194305	−	0.336547i	0.946673	+	0.322197i	$0.104421\pi$
$420$		0			0
$421$	1.30584	+	2.26178i	0.0636426	+	0.110232i	0.896091	−	0.443870i	$-0.146395\pi$
$421$	1.30584	+	2.26178i	0.0636426	+	0.110232i	−0.832448	+	0.554102i	$0.813062\pi$
$422$		0			0
$423$	10.1432	+	20.4485i	0.493177	+	0.994239i
$424$		0			0
$425$	−27.0712	+	46.8887i	−1.31315	+	2.27444i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.378950	−	12.0017i	0.0182959	−	0.579449i
$430$		0			0
$431$	0.791065	−	1.37017i	0.0381043	−	0.0659985i	−0.846344	−	0.532636i	$-0.821201\pi$
$431$	0.791065	−	1.37017i	0.0381043	−	0.0659985i	0.884449	+	0.466638i	$0.154535\pi$
$432$		0			0
$433$	−5.17110			−0.248507			−0.124254	−	0.992250i	$-0.539654\pi$
$433$	−5.17110			−0.248507			−0.124254	+	0.992250i	$0.539654\pi$
$434$		0			0
$435$	58.2966	+	36.1574i	2.79511	+	1.73361i
$436$		0			0
$437$	−0.853887	−	1.47898i	−0.0408470	−	0.0707490i
$438$		0			0
$439$	−12.4806	+	21.6170i	−0.595665	+	1.03172i	0.397788	+	0.917477i	$0.369778\pi$
$439$	−12.4806	+	21.6170i	−0.595665	+	1.03172i	−0.993453	+	0.114244i	$0.963555\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.542263	+	0.939227i	−0.0257637	+	0.0446240i	−0.878620	−	0.477522i	$-0.841535\pi$
$443$	−0.542263	+	0.939227i	−0.0257637	+	0.0446240i	0.852856	+	0.522146i	$0.174868\pi$
$444$		0			0
$445$	23.7825	+	41.1924i	1.12740	+	1.95271i
$446$		0			0
$447$	21.1315	−	11.3266i	0.999484	−	0.535728i
$448$		0			0
$449$	4.23372			0.199802			0.0999008	−	0.994997i	$-0.468147\pi$
$449$	4.23372			0.199802			0.0999008	+	0.994997i	$0.468147\pi$
$450$		0			0
$451$	3.02108	−	5.23267i	0.142257	−	0.246397i
$452$		0			0
$453$	34.9220	−	18.7184i	1.64078	−	0.879466i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.1513	−	31.4390i	0.849083	−	1.47065i	−0.0329453	−	0.999457i	$-0.510489\pi$
$457$	18.1513	−	31.4390i	0.849083	−	1.47065i	0.882028	−	0.471197i	$-0.156178\pi$
$458$		0			0
$459$	22.5833	+	16.0642i	1.05410	+	0.749814i
$460$		0			0
$461$	1.71236	+	2.96589i	0.0797524	+	0.138135i	0.903143	−	0.429340i	$-0.141254\pi$
$461$	1.71236	+	2.96589i	0.0797524	+	0.138135i	−0.823391	+	0.567475i	$0.807920\pi$
$462$		0			0
$463$	2.38499	−	4.13092i	0.110840	−	0.191980i	−0.805269	−	0.592909i	$-0.797979\pi$
$463$	2.38499	−	4.13092i	0.110840	−	0.191980i	0.916109	+	0.400929i	$0.131313\pi$
$464$		0			0
$465$	13.1520	+	8.15727i	0.609908	+	0.378284i
$466$		0			0
$467$	−10.0490	−	17.4053i	−0.465010	−	0.805422i	0.534192	−	0.845363i	$-0.320616\pi$
$467$	−10.0490	−	17.4053i	−0.465010	−	0.805422i	−0.999202	+	0.0399417i	$0.987283\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	17.0446	+	10.5716i	0.785373	+	0.487113i
$472$		0			0
$473$	16.7015	+	28.9279i	0.767936	+	1.33010i
$474$		0			0
$475$	−23.5673	−	40.8198i	−1.08134	−	1.87294i
$476$		0			0
$477$	−1.23405	−	2.48783i	−0.0565033	−	0.113910i
$478$		0			0
$479$	−16.8506			−0.769922			−0.384961	−	0.922933i	$-0.625785\pi$
$479$	−16.8506			−0.769922			−0.384961	+	0.922933i	$0.625785\pi$
$480$		0			0
$481$	−17.2388			−0.786023
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.3337	+	30.0229i	0.787084	+	1.36327i
$486$		0			0
$487$	−11.9916	+	20.7700i	−0.543389	+	0.941178i	0.455317	+	0.890329i	$0.349526\pi$
$487$	−11.9916	+	20.7700i	−0.543389	+	0.941178i	−0.998706	+	0.0508486i	$0.983807\pi$
$488$		0			0
$489$	−5.02153	−	3.11451i	−0.227082	−	0.140843i
$490$		0			0
$491$	−1.07281	+	1.85816i	−0.0484153	+	0.0838577i	−0.889217	−	0.457485i	$-0.848750\pi$
$491$	−1.07281	+	1.85816i	−0.0484153	+	0.0838577i	0.840802	+	0.541342i	$0.182084\pi$
$492$		0			0
$493$	54.2689			2.44415
$494$		0			0
$495$	−28.2883	+	42.5499i	−1.27146	+	1.91248i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−27.7154			−1.24071			−0.620357	−	0.784320i	$-0.713012\pi$
$499$	−27.7154			−1.24071			−0.620357	+	0.784320i	$0.713012\pi$
$500$		0			0
$501$	0.513814	−	16.2730i	0.0229555	−	0.727025i
$502$		0			0
$503$	−22.4265			−0.999949			−0.499974	−	0.866040i	$-0.666657\pi$
$503$	−22.4265			−0.999949			−0.499974	+	0.866040i	$0.666657\pi$
$504$		0			0
$505$	42.9090			1.90943
$506$		0			0
$507$	15.4400	+	9.57636i	0.685714	+	0.425301i
$508$		0			0
$509$	−29.3689			−1.30175			−0.650876	−	0.759184i	$-0.725598\pi$
$509$	−29.3689			−1.30175			−0.650876	+	0.759184i	$0.725598\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−21.9415	+	10.0338i	−0.968742	+	0.443004i
$514$		0			0
$515$	10.6298			0.468403
$516$		0			0
$517$	−16.6461	+	28.8318i	−0.732093	+	1.26802i
$518$		0			0
$519$	−0.350114	+	11.0885i	−0.0153683	+	0.486730i
$520$		0			0
$521$	8.25389	−	14.2962i	0.361610	−	0.626326i	−0.626616	−	0.779328i	$-0.715561\pi$
$521$	8.25389	−	14.2962i	0.361610	−	0.626326i	0.988226	+	0.153002i	$0.0488940\pi$
$522$		0			0
$523$	−22.3476	−	38.7072i	−0.977193	−	1.69255i	−0.672499	−	0.740098i	$-0.734779\pi$
$523$	−22.3476	−	38.7072i	−0.977193	−	1.69255i	−0.304695	−	0.952450i	$-0.598554\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.2433			0.533327
$528$		0			0
$529$	−22.8647			−0.994118
$530$		0			0
$531$	−2.75734	−	0.174298i	−0.119659	−	0.00756388i
$532$		0			0
$533$	−1.09394	−	1.89476i	−0.0473838	−	0.0820711i
$534$		0			0
$535$	−21.0039	−	36.3798i	−0.908078	−	1.57284i
$536$		0			0
$537$	−0.933661	+	29.5700i	−0.0402904	+	1.27604i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.0369	+	17.3844i	0.431519	+	0.747412i	0.997004	−	0.0773460i	$-0.0246446\pi$
$541$	10.0369	+	17.3844i	0.431519	+	0.747412i	−0.565486	+	0.824758i	$0.691311\pi$
$542$		0			0
$543$	−2.07597	+	1.11273i	−0.0890884	+	0.0477518i
$544$		0			0
$545$	−19.4307	+	33.6549i	−0.832319	+	1.44162i
$546$		0			0
$547$	6.35012	+	10.9987i	0.271512	+	0.470272i	0.969249	−	0.246082i	$-0.0791432\pi$
$547$	6.35012	+	10.9987i	0.271512	+	0.470272i	−0.697738	+	0.716353i	$0.745810\pi$
$548$		0			0
$549$	−8.73932	−	17.6184i	−0.372985	−	0.751933i
$550$		0			0
$551$	−23.6224	+	40.9152i	−1.00635	+	1.74305i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	62.3379	+	38.6639i	2.64610	+	1.64119i
$556$		0			0
$557$	−7.34743	+	12.7261i	−0.311321	+	0.539223i	−0.978649	−	0.205541i	$-0.934105\pi$
$557$	−7.34743	+	12.7261i	−0.311321	+	0.539223i	0.667328	+	0.744764i	$0.267438\pi$
$558$		0			0
$559$	12.0953			0.511576
$560$		0			0
$561$	−1.27566	+	40.4013i	−0.0538583	+	1.70575i
$562$		0			0
$563$	13.3930	+	23.1974i	0.564448	+	0.977653i	0.997101	+	0.0760922i	$0.0242443\pi$
$563$	13.3930	+	23.1974i	0.564448	+	0.977653i	−0.432653	+	0.901561i	$0.642422\pi$
$564$		0			0
$565$	23.8226	−	41.2620i	1.00222	−	1.73590i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.24168	+	5.61475i	−0.135898	+	0.235383i	−0.925940	−	0.377670i	$-0.876725\pi$
$569$	−3.24168	+	5.61475i	−0.135898	+	0.235383i	0.790042	+	0.613053i	$0.210059\pi$
$570$		0			0
$571$	−7.81632	−	13.5383i	−0.327103	−	0.566559i	0.654833	−	0.755774i	$-0.272739\pi$
$571$	−7.81632	−	13.5383i	−0.327103	−	0.566559i	−0.981936	+	0.189215i	$0.939406\pi$
$572$		0			0
$573$	0.977402	−	30.9553i	0.0408315	−	1.29318i
$574$		0			0
$575$	3.73363			0.155703
$576$		0			0
$577$	−14.5800	+	25.2533i	−0.606974	+	1.05131i	0.384763	+	0.923016i	$0.374283\pi$
$577$	−14.5800	+	25.2533i	−0.606974	+	1.05131i	−0.991736	+	0.128294i	$0.959050\pi$
$578$		0			0
$579$	19.1545	+	11.8802i	0.796036	+	0.493726i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.02522	−	3.50778i	0.0838759	−	0.145277i
$584$		0			0
$585$	8.22158	+	16.5746i	0.339921	+	0.685275i
$586$		0			0
$587$	2.33110	+	4.03758i	0.0962146	+	0.166649i	0.910115	−	0.414356i	$-0.135993\pi$
$587$	2.33110	+	4.03758i	0.0962146	+	0.166649i	−0.813900	+	0.581005i	$0.802660\pi$
$588$		0			0
$589$	−5.32932	+	9.23065i	−0.219591	+	0.380342i
$590$		0			0
$591$	9.71649	−	5.20808i	0.399683	−	0.214232i
$592$		0			0
$593$	15.8322	+	27.4222i	0.650150	+	1.12609i	0.983086	+	0.183144i	$0.0586275\pi$
$593$	15.8322	+	27.4222i	0.650150	+	1.12609i	−0.332936	+	0.942950i	$0.608039\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.26557	−	40.0819i	0.0517964	−	1.64044i
$598$		0			0
$599$	5.15268	+	8.92470i	0.210533	+	0.364653i	0.951881	−	0.306467i	$-0.0991468\pi$
$599$	5.15268	+	8.92470i	0.210533	+	0.364653i	−0.741349	+	0.671120i	$0.765813\pi$
$600$		0			0
$601$	4.64993	+	8.05391i	0.189674	+	0.328526i	0.945142	−	0.326661i	$-0.105923\pi$
$601$	4.64993	+	8.05391i	0.189674	+	0.328526i	−0.755467	+	0.655186i	$0.772590\pi$
$602$		0			0
$603$	−44.9355	−	2.84047i	−1.82991	−	0.115673i
$604$		0			0
$605$	−31.7064			−1.28905
$606$		0			0
$607$	−20.4968			−0.831938			−0.415969	−	0.909379i	$-0.636558\pi$
$607$	−20.4968			−0.831938			−0.415969	+	0.909379i	$0.636558\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.02757	+	10.4401i	0.243850	+	0.422360i
$612$		0			0
$613$	7.17240	−	12.4230i	0.289691	−	0.501759i	−0.684045	−	0.729440i	$-0.739781\pi$
$613$	7.17240	−	12.4230i	0.289691	−	0.501759i	0.973736	+	0.227681i	$0.0731143\pi$
$614$		0			0
$615$	−0.293809	+	9.30522i	−0.0118475	+	0.375223i
$616$		0			0
$617$	−6.47499	+	11.2150i	−0.260673	+	0.451499i	−0.966421	−	0.256964i	$-0.917278\pi$
$617$	−6.47499	+	11.2150i	−0.260673	+	0.451499i	0.705748	+	0.708463i	$0.250611\pi$
$618$		0			0
$619$	35.3980			1.42277			0.711383	−	0.702804i	$-0.248069\pi$
$619$	35.3980			1.42277			0.711383	+	0.702804i	$0.248069\pi$
$620$		0			0
$621$	0.180700	−	1.90258i	0.00725124	−	0.0763479i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	27.2920			1.09168
$626$		0			0
$627$	−29.9047	−	18.5478i	−1.19428	−	0.740728i
$628$		0			0
$629$	58.0310			2.31385
$630$		0			0
$631$	33.1936			1.32141			0.660707	−	0.750644i	$-0.270256\pi$
$631$	33.1936			1.32141			0.660707	+	0.750644i	$0.270256\pi$
$632$		0			0
$633$	−0.620668	+	19.6572i	−0.0246693	+	0.781303i
$634$		0			0
$635$	51.3824			2.03905
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.15608	+	12.2680i	−0.322649	+	0.485314i
$640$		0			0
$641$	−0.239269			−0.00945056			−0.00472528	−	0.999989i	$-0.501504\pi$
$641$	−0.239269			−0.00945056			−0.00472528	+	0.999989i	$0.501504\pi$
$642$		0			0
$643$	4.57211	−	7.91913i	0.180307	−	0.312300i	−0.761678	−	0.647955i	$-0.775624\pi$
$643$	4.57211	−	7.91913i	0.180307	−	0.312300i	0.941985	+	0.335655i	$0.108958\pi$
$644$		0			0
$645$	−43.7382	−	27.1278i	−1.72219	−	1.06816i
$646$		0			0
$647$	3.15607	−	5.46648i	0.124078	−	0.214909i	−0.797294	−	0.603591i	$-0.793736\pi$
$647$	3.15607	−	5.46648i	0.124078	−	0.214909i	0.921372	+	0.388682i	$0.127069\pi$
$648$		0			0
$649$	−2.01484	−	3.48980i	−0.0790893	−	0.136987i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.55775			−0.178359			−0.0891793	−	0.996016i	$-0.528424\pi$
$653$	−4.55775			−0.178359			−0.0891793	+	0.996016i	$0.528424\pi$
$654$		0			0
$655$	19.8003			0.773662
$656$		0			0
$657$	−10.0877	−	20.3367i	−0.393560	−	0.793411i
$658$		0			0
$659$	−16.4631	−	28.5149i	−0.641311	−	1.11078i	−0.985140	−	0.171751i	$-0.945058\pi$
$659$	−16.4631	−	28.5149i	−0.641311	−	1.11078i	0.343829	−	0.939032i	$-0.388276\pi$
$660$		0			0
$661$	0.270668	+	0.468811i	0.0105278	+	0.0182346i	0.871241	−	0.490855i	$-0.163316\pi$
$661$	0.270668	+	0.468811i	0.0105278	+	0.0182346i	−0.860714	+	0.509090i	$0.829982\pi$
$662$		0			0
$663$	12.4385	+	7.71473i	0.483070	+	0.299615i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.87118	−	3.24097i	−0.0724523	−	0.125491i
$668$		0			0
$669$	39.2137	+	24.3216i	1.51609	+	0.940326i
$670$		0			0
$671$	14.3422	−	24.8415i	0.553676	−	0.958994i
$672$		0			0
$673$	−11.8205	−	20.4737i	−0.455647	−	0.789204i	0.543078	−	0.839682i	$-0.317259\pi$
$673$	−11.8205	−	20.4737i	−0.455647	−	0.789204i	−0.998725	+	0.0504780i	$0.983926\pi$
$674$		0			0
$675$	4.98733	−	52.5113i	0.191962	−	2.02116i
$676$		0			0
$677$	−1.36494	+	2.36415i	−0.0524591	+	0.0908618i	−0.891062	−	0.453881i	$-0.850039\pi$
$677$	−1.36494	+	2.36415i	−0.0524591	+	0.0908618i	0.838603	+	0.544742i	$0.183373\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	25.3454	−	13.5853i	0.971239	−	0.520589i
$682$		0			0
$683$	15.9640	−	27.6504i	0.610844	−	1.05801i	−0.380254	−	0.924882i	$-0.624164\pi$
$683$	15.9640	−	27.6504i	0.610844	−	1.05801i	0.991098	−	0.133131i	$-0.0425032\pi$
$684$		0			0
$685$	−51.9417			−1.98459
$686$		0			0
$687$	22.1377	−	11.8659i	0.844605	−	0.452712i
$688$		0			0
$689$	−0.733335	−	1.27017i	−0.0279378	−	0.0483897i
$690$		0			0
$691$	−1.19103	+	2.06292i	−0.0453089	+	0.0784773i	−0.887790	−	0.460248i	$-0.847761\pi$
$691$	−1.19103	+	2.06292i	−0.0453089	+	0.0784773i	0.842482	+	0.538725i	$0.181094\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.9034	+	32.7417i	−0.717048	+	1.24196i
$696$		0			0
$697$	3.68252	+	6.37831i	0.139485	+	0.241596i
$698$		0			0
$699$	−23.5219	−	14.5890i	−0.889680	−	0.551808i
$700$		0			0
$701$	50.3767			1.90270			0.951350	−	0.308111i	$-0.0996968\pi$
$701$	50.3767			1.90270			0.951350	+	0.308111i	$0.0996968\pi$
$702$		0			0
$703$	−25.2599	+	43.7515i	−0.952697	+	1.65012i
$704$		0			0
$705$	1.61888	−	51.2715i	0.0609705	−	1.93100i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−20.1600	+	34.9182i	−0.757126	+	1.31138i	0.187184	+	0.982325i	$0.440064\pi$
$709$	−20.1600	+	34.9182i	−0.757126	+	1.31138i	−0.944310	+	0.329056i	$0.893269\pi$
$710$		0			0
$711$	2.63346	+	5.30903i	0.0987626	+	0.199104i
$712$		0			0
$713$	−0.422146	−	0.731178i	−0.0158095	−	0.0273828i
$714$		0			0
$715$	−13.4926	+	23.3698i	−0.504593	+	0.873981i
$716$		0			0
$717$	−1.04840	+	33.2040i	−0.0391533	+	1.24003i
$718$		0			0
$719$	−17.0446	−	29.5222i	−0.635658	−	1.10099i	−0.986375	−	0.164510i	$-0.947396\pi$
$719$	−17.0446	−	29.5222i	−0.635658	−	1.10099i	0.350718	−	0.936481i	$-0.385938\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−35.6563	+	19.1119i	−1.32607	+	0.710781i
$724$		0			0
$725$	−51.6446	−	89.4510i	−1.91803	−	3.32213i
$726$		0			0
$727$	−10.9453	−	18.9578i	−0.405938	−	0.703105i	0.588492	−	0.808503i	$-0.299722\pi$
$727$	−10.9453	−	18.9578i	−0.405938	−	0.703105i	−0.994430	+	0.105398i	$0.966388\pi$
$728$		0			0
$729$	−26.5172	−	5.08288i	−0.982120	−	0.188255i
$730$		0			0
$731$	−40.7163			−1.50595
$732$		0			0
$733$	8.68831			0.320910			0.160455	−	0.987043i	$-0.448704\pi$
$733$	8.68831			0.320910			0.160455	+	0.987043i	$0.448704\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32.8351	−	56.8721i	−1.20950	−	2.09491i
$738$		0			0
$739$	−3.34692	+	5.79704i	−0.123119	+	0.213248i	−0.920996	−	0.389572i	$-0.872623\pi$
$739$	−3.34692	+	5.79704i	−0.123119	+	0.213248i	0.797877	+	0.602820i	$0.205956\pi$
$740$		0			0
$741$	−11.2307	+	6.01969i	−0.412569	+	0.221139i
$742$		0			0
$743$	21.5001	−	37.2392i	0.788761	−	1.36617i	−0.137965	−	0.990437i	$-0.544056\pi$
$743$	21.5001	−	37.2392i	0.788761	−	1.36617i	0.926726	−	0.375737i	$-0.122611\pi$
$744$		0			0
$745$	−53.8807			−1.97404
$746$		0			0
$747$	1.51504	+	0.0957691i	0.0554324	+	0.00350401i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.7274			−0.610391			−0.305196	−	0.952290i	$-0.598722\pi$
$751$	−16.7274			−0.610391			−0.305196	+	0.952290i	$0.598722\pi$
$752$		0			0
$753$	46.5027	−	24.9257i	1.69465	−	0.908342i
$754$		0			0
$755$	−89.0438			−3.24064
$756$		0			0
$757$	−4.68561			−0.170301			−0.0851507	−	0.996368i	$-0.527137\pi$
$757$	−4.68561			−0.170301			−0.0851507	+	0.996368i	$0.527137\pi$
$758$		0			0
$759$	2.45678	−	1.31684i	0.0891754	−	0.0477984i
$760$		0			0
$761$	51.6484			1.87225			0.936127	−	0.351663i	$-0.114384\pi$
$761$	51.6484			1.87225			0.936127	+	0.351663i	$0.114384\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−27.6763	−	55.7950i	−1.00064	−	2.01727i
$766$		0			0
$767$	−1.45915			−0.0526870
$768$		0			0
$769$	−15.3910	+	26.6580i	−0.555014	+	0.961313i	0.442888	+	0.896577i	$0.353954\pi$
$769$	−15.3910	+	26.6580i	−0.555014	+	0.961313i	−0.997902	+	0.0647361i	$0.979379\pi$
$770$		0			0
$771$	10.3942	−	5.57131i	0.374336	−	0.200646i
$772$		0			0
$773$	13.5259	−	23.4275i	0.486491	−	0.842627i	−0.513388	−	0.858156i	$-0.671610\pi$
$773$	13.5259	−	23.4275i	0.486491	−	0.842627i	0.999879	+	0.0155292i	$0.00494329\pi$
$774$		0			0
$775$	−11.6512	−	20.1805i	−0.418525	−	0.724907i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.41177			−0.229725
$780$		0			0
$781$	−21.4866			−0.768852
$782$		0			0
$783$	−48.0818	+	21.9877i	−1.71830	+	0.785777i
$784$		0			0
$785$	−22.5370	−	39.0352i	−0.804380	−	1.39323i
$786$		0			0
$787$	−17.5997	−	30.4837i	−0.627363	−	1.08662i	−0.988079	−	0.153949i	$-0.950801\pi$
$787$	−17.5997	−	30.4837i	−0.627363	−	1.08662i	0.360716	−	0.932676i	$-0.382532\pi$
$788$		0			0
$789$	−7.02230	+	3.76398i	−0.250000	+	0.134001i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.19335	−	8.99514i	−0.184421	−	0.319427i
$794$		0			0
$795$	−0.196958	+	6.23786i	−0.00698538	+	0.221234i
$796$		0			0
$797$	23.8268	−	41.2692i	0.843988	−	1.46183i	−0.0425084	−	0.999096i	$-0.513535\pi$
$797$	23.8268	−	41.2692i	0.843988	−	1.46183i	0.886497	−	0.462735i	$-0.153132\pi$
$798$		0			0
$799$	−20.2906	−	35.1443i	−0.717829	−	1.24332i
$800$		0			0
$801$	−36.5862	−	2.31270i	−1.29271	−	0.0817151i
$802$		0			0
$803$	16.5551	−	28.6743i	0.584217	−	1.01189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.464721	+	14.7182i	−0.0163590	+	0.518105i
$808$		0			0
$809$	−9.87711	+	17.1077i	−0.347261	+	0.601473i	−0.985762	−	0.168148i	$-0.946221\pi$
$809$	−9.87711	+	17.1077i	−0.347261	+	0.601473i	0.638501	+	0.769621i	$0.279555\pi$
$810$		0			0
$811$	49.2424			1.72913			0.864567	−	0.502518i	$-0.167593\pi$
$811$	49.2424			1.72913			0.864567	+	0.502518i	$0.167593\pi$
$812$		0			0
$813$	9.69086	+	6.01057i	0.339873	+	0.210800i
$814$		0			0
$815$	6.63967	+	11.5002i	0.232577	+	0.402836i
$816$		0			0
$817$	17.7231	−	30.6974i	0.620054	−	1.07397i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.00013	+	8.66048i	−0.174506	+	0.302253i	−0.939990	−	0.341202i	$-0.889166\pi$
$821$	−5.00013	+	8.66048i	−0.174506	+	0.302253i	0.765484	+	0.643455i	$0.222499\pi$
$822$		0			0
$823$	17.5138	+	30.3348i	0.610493	+	1.05741i	0.991157	+	0.132692i	$0.0423621\pi$
$823$	17.5138	+	30.3348i	0.610493	+	1.05741i	−0.380664	+	0.924713i	$0.624305\pi$
$824$		0			0
$825$	67.8072	−	36.3449i	2.36074	−	1.26537i
$826$		0			0
$827$	−22.7079			−0.789631			−0.394816	−	0.918760i	$-0.629192\pi$
$827$	−22.7079			−0.789631			−0.394816	+	0.918760i	$0.629192\pi$
$828$		0			0
$829$	−6.22083	+	10.7748i	−0.216058	+	0.374224i	−0.953599	−	0.301078i	$-0.902653\pi$
$829$	−6.22083	+	10.7748i	−0.216058	+	0.374224i	0.737541	+	0.675302i	$0.235987\pi$
$830$		0			0
$831$	−17.2041	+	9.22147i	−0.596803	+	0.319889i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.2944	+	31.6869i	−0.633105	+	1.09657i
$836$		0			0
$837$	−10.8475	+	4.96053i	−0.374944	+	0.171461i
$838$		0			0
$839$	13.8249	+	23.9455i	0.477290	+	0.826690i	0.999661	−	0.0260281i	$-0.00828595\pi$
$839$	13.8249	+	23.9455i	0.477290	+	0.826690i	−0.522372	+	0.852718i	$0.674953\pi$
$840$		0			0
$841$	−37.2652	+	64.5453i	−1.28501	+	2.22570i
$842$		0			0
$843$	22.1006	+	13.7075i	0.761186	+	0.472112i
$844$		0			0
$845$	−20.4153	−	35.3604i	−0.702309	−	1.21643i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	21.5977	+	13.3956i	0.741232	+	0.459735i
$850$		0			0
$851$	−2.00089	−	3.46564i	−0.0685896	−	0.118801i
$852$		0			0
$853$	22.0459	+	38.1847i	0.754839	+	1.30742i	0.945454	+	0.325754i	$0.105618\pi$
$853$	22.0459	+	38.1847i	0.754839	+	1.30742i	−0.190616	+	0.981665i	$0.561048\pi$
$854$		0			0
$855$	54.1127	+	3.42059i	1.85062	+	0.116982i
$856$		0			0
$857$	26.7676			0.914363			0.457182	−	0.889373i	$-0.348859\pi$
$857$	26.7676			0.914363			0.457182	+	0.889373i	$0.348859\pi$
$858$		0			0
$859$	20.1901			0.688879			0.344439	−	0.938809i	$-0.388069\pi$
$859$	20.1901			0.688879			0.344439	+	0.938809i	$0.388069\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.74538	−	8.21923i	−0.161534	−	0.279786i	0.773885	−	0.633327i	$-0.218311\pi$
$863$	−4.74538	−	8.21923i	−0.161534	−	0.279786i	−0.935419	+	0.353541i	$0.884978\pi$
$864$		0			0
$865$	12.4659	−	21.5915i	0.423852	−	0.734133i
$866$		0			0
$867$	−16.8489	−	10.4502i	−0.572218	−	0.354908i
$868$		0			0
$869$	−4.32182	+	7.48560i	−0.146608	+	0.253932i
$870$		0			0
$871$	−23.7793			−0.805731
$872$		0			0
$873$	−26.6657	−	1.68560i	−0.902497	−	0.0570488i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	29.2455			0.987549			0.493774	−	0.869590i	$-0.335617\pi$
$877$	29.2455			0.987549			0.493774	+	0.869590i	$0.335617\pi$
$878$		0			0
$879$	1.02652	−	32.5111i	0.0346238	−	1.09657i
$880$		0			0
$881$	−37.2768			−1.25589			−0.627944	−	0.778259i	$-0.716103\pi$
$881$	−37.2768			−1.25589			−0.627944	+	0.778259i	$0.716103\pi$
$882$		0			0
$883$	−56.9436			−1.91630			−0.958152	−	0.286260i	$-0.907588\pi$
$883$	−56.9436			−1.91630			−0.958152	+	0.286260i	$0.907588\pi$
$884$		0			0
$885$	5.27649	+	3.27264i	0.177367	+	0.110009i
$886$		0			0
$887$	9.92253			0.333166			0.166583	−	0.986027i	$-0.446727\pi$
$887$	9.92253			0.333166			0.166583	+	0.986027i	$0.446727\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−15.2389	−	36.3121i	−0.510522	−	1.21650i
$892$		0			0
$893$	35.3287			1.18223
$894$		0			0
$895$	33.2431	−	57.5787i	1.11119	−	1.92465i
$896$		0			0
$897$	0.0318536	−	1.00884i	0.00106356	−	0.0336840i
$898$		0			0
$899$	−11.6785	+	20.2277i	−0.389499	+	0.674632i
$900$		0			0
$901$	2.46862	+	4.27577i	0.0822416	+	0.142447i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.29328			0.175955
$906$		0			0
$907$	−24.5775			−0.816081			−0.408040	−	0.912964i	$-0.633788\pi$
$907$	−24.5775			−0.816081			−0.408040	+	0.912964i	$0.633788\pi$
$908$		0			0
$909$	−18.3093	+	27.5400i	−0.607280	+	0.913443i
$910$		0			0
$911$	9.73496	+	16.8614i	0.322534	+	0.558645i	0.981010	−	0.193957i	$-0.0621321\pi$
$911$	9.73496	+	16.8614i	0.322534	+	0.558645i	−0.658476	+	0.752601i	$0.728799\pi$
$912$		0			0
$913$	1.10707	+	1.91749i	0.0366385	+	0.0634598i
$914$		0			0
$915$	−1.39482	+	44.1754i	−0.0461114	+	1.46040i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	6.61992	+	11.4660i	0.218371	+	0.378230i	0.954310	−	0.298818i	$-0.0965923\pi$
$919$	6.61992	+	11.4660i	0.218371	+	0.378230i	−0.735939	+	0.677048i	$0.763259\pi$
$920$		0			0
$921$	44.1832	−	23.6824i	1.45589	−	0.780361i
$922$		0			0
$923$	−3.89017	+	6.73798i	−0.128047	+	0.221783i
$924$		0			0
$925$	−55.2247	−	95.6519i	−1.81578	−	3.14502i
$926$		0			0
$927$	−4.53572	+	6.82242i	−0.148973	+	0.224078i
$928$		0			0
$929$	15.8682	−	27.4845i	0.520618	−	0.901737i	−0.479095	−	0.877763i	$-0.659035\pi$
$929$	15.8682	−	27.4845i	0.520618	−	0.901737i	0.999713	−	0.0239734i	$-0.00763170\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−20.0088	−	12.4101i	−0.655057	−	0.406287i
$934$		0			0
$935$	45.4199	−	78.6696i	1.48539	−	2.57277i
$936$		0			0
$937$	13.5019			0.441087			0.220543	−	0.975377i	$-0.429217\pi$
$937$	13.5019			0.441087			0.220543	+	0.975377i	$0.429217\pi$
$938$		0			0
$939$	−0.757852	+	24.0020i	−0.0247316	+	0.783274i
$940$		0			0
$941$	−19.8286	−	34.3441i	−0.646394	−	1.11959i	−0.983978	−	0.178291i	$-0.942943\pi$
$941$	−19.8286	−	34.3441i	−0.646394	−	1.11959i	0.337584	−	0.941295i	$-0.390390\pi$
$942$		0			0
$943$	0.253944	−	0.439845i	0.00826957	−	0.0143233i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.5172	−	52.8573i	0.991675	−	1.71763i	0.384325	−	0.923198i	$-0.374434\pi$
$947$	30.5172	−	52.8573i	0.991675	−	1.71763i	0.607350	−	0.794434i	$-0.292232\pi$
$948$		0			0
$949$	−5.99464	−	10.3830i	−0.194594	−	0.337047i
$950$		0			0
$951$	−1.26190	+	39.9656i	−0.0409198	+	1.29597i
$952$		0			0
$953$	5.22726			0.169328			0.0846638	−	0.996410i	$-0.473018\pi$
$953$	5.22726			0.169328			0.0846638	+	0.996410i	$0.473018\pi$
$954$		0			0
$955$	−34.8005	+	60.2762i	−1.12612	+	1.95049i
$956$		0			0
$957$	−65.5320	−	40.6450i	−2.11835	−	1.31387i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.8653	−	22.2833i	0.415009	−	0.718817i
$962$		0			0
$963$	32.3118	+	2.04250i	1.04123	+	0.0658186i
$964$		0			0
$965$	−25.3269	−	43.8674i	−0.815301	−	1.41214i
$966$		0			0
$967$	10.2035	−	17.6729i	0.328121	−	0.568323i	−0.654018	−	0.756479i	$-0.726918\pi$
$967$	10.2035	−	17.6729i	0.328121	−	0.568323i	0.982139	+	0.188156i	$0.0602511\pi$
$968$		0			0
$969$	37.8057	−	20.2640i	1.21449	−	0.650975i
$970$		0			0
$971$	0.589402	+	1.02087i	0.0189148	+	0.0327614i	0.875328	−	0.483530i	$-0.160646\pi$
$971$	0.589402	+	1.02087i	0.0189148	+	0.0327614i	−0.856413	+	0.516291i	$0.827312\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.879160	−	27.8439i	0.0281556	−	0.891718i
$976$		0			0
$977$	−4.10487	−	7.10984i	−0.131326	−	0.227464i	0.792862	−	0.609402i	$-0.208590\pi$
$977$	−4.10487	−	7.10984i	−0.131326	−	0.227464i	−0.924188	+	0.381938i	$0.875257\pi$
$978$		0			0
$979$	−26.7342	−	46.3049i	−0.854427	−	1.47991i
$980$		0			0
$981$	−13.3094	−	26.8316i	−0.424937	−	0.856667i
$982$		0			0
$983$	1.50696			0.0480646			0.0240323	−	0.999711i	$-0.492350\pi$
$983$	1.50696			0.0480646			0.0240323	+	0.999711i	$0.492350\pi$
$984$		0			0
$985$	−24.7750			−0.789397
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.40389	+	2.43160i	0.0446410	+	0.0773204i
$990$		0			0
$991$	−16.2229	+	28.0990i	−0.515339	+	0.892593i	0.484503	+	0.874790i	$0.339001\pi$
$991$	−16.2229	+	28.0990i	−0.515339	+	0.892593i	−0.999842	+	0.0178030i	$0.994333\pi$
$992$		0			0
$993$	0.855615	−	27.0982i	0.0271521	−	0.859935i
$994$		0			0
$995$	−45.0608	+	78.0476i	−1.42852	+	2.47428i
$996$		0			0
$997$	12.5240			0.396638			0.198319	−	0.980138i	$-0.436452\pi$
$997$	12.5240			0.396638			0.198319	+	0.980138i	$0.436452\pi$
$998$		0			0
$999$	−51.4150	+	23.5120i	−1.62670	+	0.743886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.j.949.11		24
3.2	odd	2		5292.2.l.j.361.12		24
7.2	even	3		1764.2.i.j.373.6		24
7.3	odd	6		1764.2.j.i.589.10	yes	24
7.4	even	3		1764.2.j.i.589.3	✓	24
7.5	odd	6		1764.2.i.j.373.7		24
7.6	odd	2	inner	1764.2.l.j.949.2		24
9.2	odd	6		5292.2.i.j.2125.1		24
9.7	even	3		1764.2.i.j.1537.6		24
21.2	odd	6		5292.2.i.j.1549.1		24
21.5	even	6		5292.2.i.j.1549.12		24
21.11	odd	6		5292.2.j.i.1765.1		24
21.17	even	6		5292.2.j.i.1765.12		24
21.20	even	2		5292.2.l.j.361.1		24
63.2	odd	6		5292.2.l.j.3313.12		24
63.11	odd	6		5292.2.j.i.3529.1		24
63.16	even	3	inner	1764.2.l.j.961.11		24
63.20	even	6		5292.2.i.j.2125.12		24
63.25	even	3		1764.2.j.i.1177.3	yes	24
63.34	odd	6		1764.2.i.j.1537.7		24
63.38	even	6		5292.2.j.i.3529.12		24
63.47	even	6		5292.2.l.j.3313.1		24
63.52	odd	6		1764.2.j.i.1177.10	yes	24
63.61	odd	6	inner	1764.2.l.j.961.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.6		24	7.2	even	3
1764.2.i.j.373.7		24	7.5	odd	6
1764.2.i.j.1537.6		24	9.7	even	3
1764.2.i.j.1537.7		24	63.34	odd	6
1764.2.j.i.589.3	✓	24	7.4	even	3
1764.2.j.i.589.10	yes	24	7.3	odd	6
1764.2.j.i.1177.3	yes	24	63.25	even	3
1764.2.j.i.1177.10	yes	24	63.52	odd	6
1764.2.l.j.949.2		24	7.6	odd	2	inner
1764.2.l.j.949.11		24	1.1	even	1	trivial
1764.2.l.j.961.2		24	63.61	odd	6	inner
1764.2.l.j.961.11		24	63.16	even	3	inner
5292.2.i.j.1549.1		24	21.2	odd	6
5292.2.i.j.1549.12		24	21.5	even	6
5292.2.i.j.2125.1		24	9.2	odd	6
5292.2.i.j.2125.12		24	63.20	even	6
5292.2.j.i.1765.1		24	21.11	odd	6
5292.2.j.i.1765.12		24	21.17	even	6
5292.2.j.i.3529.1		24	63.11	odd	6
5292.2.j.i.3529.12		24	63.38	even	6
5292.2.l.j.361.1		24	21.20	even	2
5292.2.l.j.361.12		24	3.2	odd	2
5292.2.l.j.3313.1		24	63.47	even	6
5292.2.l.j.3313.12		24	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52658 - 0.818256i) q^{3} -3.89246 q^{5} +(1.66092 - 2.49827i) q^{9} +4.37557 q^{11} +(0.792201 - 1.37213i) q^{13} +(-5.94217 + 3.18503i) q^{15} +(-2.66678 + 4.61900i) q^{17} +(-2.32161 - 4.02115i) q^{19} +0.367799 q^{23} +10.1513 q^{25} +(0.491301 - 5.17287i) q^{27} +(-5.08750 - 8.81180i) q^{29} +(-1.14776 - 1.98798i) q^{31} +(6.67967 - 3.58033i) q^{33} +(-5.44017 - 9.42265i) q^{37} +(0.0866059 - 2.74290i) q^{39} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(-6.46505 + 9.72443i) q^{45} +(-3.80432 + 6.58928i) q^{47} +(-0.291541 + 9.23339i) q^{51} +(0.462847 - 0.801674i) q^{53} -17.0317 q^{55} +(-6.83447 - 4.23895i) q^{57} +(-0.460475 - 0.797565i) q^{59} +(3.27780 - 5.67731i) q^{61} +(-3.08361 + 5.34097i) q^{65} +(-7.50420 - 12.9976i) q^{67} +(0.561476 - 0.300954i) q^{69} -4.91059 q^{71} +(3.78353 - 6.55327i) q^{73} +(15.4968 - 8.30634i) q^{75} +(-0.987715 + 1.71077i) q^{79} +(-3.48272 - 8.29883i) q^{81} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +(-14.9768 - 9.28908i) q^{87} +(-6.10987 - 10.5826i) q^{89} +(-3.37883 - 2.09566i) q^{93} +(9.03679 + 15.6522i) q^{95} +(-4.45315 - 7.71308i) q^{97} +(7.26745 - 10.9314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95}+ \cdots - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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